Separation Properties of Sets of Probability Measures
نویسنده
چکیده
This paper analyzes independence concepts for sets of probability measures associated with directed acyclic graphs. The paper shows that epistemic independence and the standard Markov condition violate desirable separation properties. The adoption of a contraction condition leads to d-separation but still fails to guarantee a belief separa tion property. To overcome this unsatisfac tory situation, a strong Markov condition is proposed, based on epistemic independence. The main result is that the strong Markov condition leads to strong independence and does enforce separation properties; this re sult implies that (1) separation properties of Bayesian networks do extend to epistemic in dependence and sets of probability measures, and (2) strong independence has a clear justi fication based on epistemic independence and the strong Markov condition.
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